Fungrim entry: def588

Symbol: Binomial ${n \choose k}$ Binomial coefficient
Domain Codomain
$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$ ${n \choose k} \in \mathbb{Z}_{\ge 0}$
$n \in \mathbb{C} \;\mathbin{\operatorname{and}}\; k \in \mathbb{Z}_{\ge 0}$ ${n \choose k} \in \mathbb{C}$
Table data: $\left(P, Q\right)$ such that $\left(P\right) \;\implies\; \left(Q\right)$
Definitions:
Fungrim symbol Notation Short description
Binomial${n \choose k}$ Binomial coefficient
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
CC$\mathbb{C}$ Complex numbers
Source code for this entry:
Entry(ID("def588"),
SymbolDefinition(Binomial, Binomial(n, k), "Binomial coefficient"),
Table(TableRelation(Tuple(P, Q), Implies(P, Q)), TableHeadings(Description("Domain"), Description("Codomain")), List(Tuple(And(Element(n, ZZGreaterEqual(0)), Element(k, ZZGreaterEqual(0))), Element(Binomial(n, k), ZZGreaterEqual(0))), Tuple(And(Element(n, CC), Element(k, ZZGreaterEqual(0))), Element(Binomial(n, k), CC)))))

Topics using this entry

Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC